Torque Converter Half-Section

The three blade rows and Euler's equation

The converter is a closed oil circuit of three rows: the pump (turned by the engine), the turbine (connected to the gearbox) and the stator (held by a one-way clutch). For each row the torque on the fluid is its change of angular momentum, T = ρ Q (rout cu,out - rin cu,in), where cu is the tangential speed of the oil and Q the circulation flow. Pump exit swirl is cu2p = σ ωp r2 - (Q/A) cot βp; the turbine exit swirl follows its own blade angle, cu2t = σ ωt r1 - (Q/A) cot βt, and the stator turns the flow forward, cu2s = (Q/A) cot αs.

Torque multiplication

Because the three torques on the fluid must add to zero, Tt = Tp + Ts. At stall the turbine throws oil back with a strong backward swirl and the stator redirects it forward into the pump, so the stator reaction adds to the turbine torque: the torque ratio TR = Tt/Tp is about 2.2 here. As the turbine speeds up the backward swirl shrinks, the stator reaction falls to zero at the coupling point, the one-way clutch lets the stator freewheel, and the converter behaves as a plain fluid coupling with TR = 1 and efficiency equal to the speed ratio.

Circulation flow from the energy balance

The circulation Q is not set by hand. Mechanical power in minus power out must equal the hydraulic losses, Tp ωp - Tt ωt = Pshock + Pfriction, with shock loss ½ ρ Q ξs Σ (Δwu)2 where the oil meets a blade at the wrong angle, and friction loss ½ ρ Q ξf Σ w2. Dividing by Q leaves a quadratic in Q that is solved by bisection every step. Efficiency is η = Tt ωt / (Tp ωp) = TR · SR.

Capacity and similarity

Pump torque scales as Tp ∝ ρ ω2 D5, so a 10 % larger torus absorbs 61 % more torque and the engine is pulled to a lower stall speed. Converter makers quote the capacity factor K = np / √Tp, a function of speed ratio only.

Lock-up, heat and the vehicle

The lock-up clutch bridges pump and turbine mechanically; when it holds, slip is zero, there is no oil loss and fuel use falls. The oil is heated by the hydraulic loss plus any clutch slip power and cooled by the oil cooler, C dT/dt = Ploss - G (T - 35 C). Engine, turbine side and vehicle (mass, rolling resistance 1.2 %, drag, grade) are integrated together; shifting rescales the equivalent inertia.

Honest simplifications

A one-dimensional mean-streamline model with fixed blade geometry, constant loss coefficients and no leakage, cavitation or fluid-temperature viscosity effects. The gear train in the 3D scene is illustrative (its tooth counts do not match the shift ratios). Numbers are of the right order for a passenger-car converter, not data for any product.